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191T8 - ECON191(Spring 2010 22 23 26.4.2010(Tutorial 8...

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1 ECON191 (Spring 2010) 22, 23 & 26.4.2010 (Tutorial 8) Chapter 11 Uncertainty (Chapter 5 of Textbook) Expected value : Probability weighted average of the payoffs associated with all possible outcomes E ( X ) = Pr 1 X 1 + Pr 2 X 2 + … + Pr n X n Preference toward risk A consumer gets utility from income, and payoff measured in terms of utility Expected utility : sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur E ( U ) = Pr of U 1 ( U 1 ) + Pr of U 2 ( U 2 ) + … + Pr of U n ( U n ) Example : No Gamble: sure income of 50 which yields U (50) Gamble: win 100 with probability 0.5 and win nothing with probability 0.5 Expected Utility = EU = 0.5 U (0) + 0.5 U (100) Utility Wealth EU U (50) 50 0 100 U (100) U (0) U (Wealth) Utility Wealth EU U (50) 50 0 100 U (100) U (0) U (Wealth) Risk Averse Diminishing marginal utility of wealth EU of the gamble < utility of a certain wealth EU < U (50) Prefer certain income than uncertain (risky) income with the same expected value Risk Neutral Constant marginal utility of wealth. EU of the gamble = utility of a certain wealth EU = U (50) Indifference between certain income than uncertain income with the same expected value Risk Loving Increasing marginal utility of wealth EU of the gamble > utility of a certain wealth EU > U (50) Prefer uncertain income than certain income with the same expected value Utility Wealth EU = U (50) 50 0 100 U (100) U (0) U(Wealth)
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2 Example : Buying an insurance Owing a house: land = 20 and house = 80, total wealth = 100 Probability of fire = 0.2, if fire occurs, wealth = 20 Expected wealth = 0.2 (20) + 0.8(100) = 84 No Insurance Expected Utiltiy = EU = 0.2 U (20) + 0.8 U (100) Insurance Premium = 20 and compensation = 80 No Fire: Wealth = 100 premium = 80 Fire: Wealth = 100 premium loss + compensation = 80 Risk premium : the maximum amount of money that a risk-adverse person is willing to pay to avoid taking risk Risk Premium = (expected income) (the certain income that yields the same expected utility as the risky income)
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